This research is intended to apply techniques of mathematical modeling and statistical estimation to understand the natural history of lung cancer and the impact of screening on mortality from the disease. Detailed data from the Memorial Sloan-Kettering Early Lung Cancer Detection program are available for model validation and parameter estimation. In that program, 10,040 high-risk volunteers were enrolled and screened annually for at least five years with chest Xrays. Half of them, allocated randomly, were asked to submit sputum specimens three times a year. All detected cancers were treated, and detailed records of test results, the characteristics of the cancers, and follow-up data were maintained. A mathematical model of the progression kinetics of lung cancer in this periodically screened population was proposed. It was assumed that the development of a cancer is a stochastic process with two stages, early and advanced, characterized by mean durations, detection probabilities, and cure probabilities. Confidence regions for these parameters were estimated, using a number of novel techniques. It was found that the mean duration of the early stage is at least 5 years, detectability is of the order of magnitude of 0.5, and curability is less than 0.4. It is now proposed that the mathematical model be refined and improved in the following ways: (1) introduction of tumor growth kinetics, (2) dependence of detectability on tumor size, (3) statistical dependence of detection in successive screens, (4) modeling of two different screening modalities (Xray and sputum) with different frequencies. It is expected that the results of this study will help to answer controversial questions of whether or not screening for lung cancer is beneficial.